diff --git a/jan-may-2022-latex/AE21B107/AE21B107.tex b/jan-may-2022-latex/AE21B107/AE21B107.tex index 056fbca..6787a9a 100644 --- a/jan-may-2022-latex/AE21B107/AE21B107.tex +++ b/jan-may-2022-latex/AE21B107/AE21B107.tex @@ -1,2 +1,52 @@ \section{AE21B107} -Student shall edit this file and include stuff for the assignment + +\subsection*{\centering{Stefan-Boltzmann law}} + +This law was formulated by Austrian physicist Josef Stefan in 1879 as a result of experimental studies. The same law, in 1884, was derived by Austrian physicist Ludwig Boltzmann from thermodynamic considerations. + +Stefan-Boltzmann law states that the total radiant heat energy emitted per unit time from a surface is proportional to the fourth power of its temperature (in Kelvins i.e. Absolute temperature). + +The emissivity of blackbody, a theoretical body considered to absorb all radiations incident on it, is 1 and that for ordinary body is between 0 and 1. + +\begin{equation} + \text{E} = {\sigma}{eT^4} +\end{equation} + +where $\sigma$ is known as Stefan-Boltzmann constant. + +\begin{equation*} + {\sigma} = 5.67 \times 10^{-8} +\end{equation*} + +Other forms of this equation can be represented as, + +\begin{equation} + \frac{dq}{dt} = {\sigma}{eT^4} +\end{equation} + +\begin{equation} + \frac{dQ}{dt} = {\sigma}{eAT^4} +\end{equation} + +The symbols used are as follows, + +\begin{table}[h] + \centering + \begin{tabular}{|c|l|} + \hline + E & Radiant heat energy emitted per unit area per second \\ + q & Radiant heat energy per unit area \\ + Q & Radiant heat energy\\ + A & Area of the radiant surface\\ + T & Absolute Temperature of the body\\ + e & Emissivity of the body\\ + $\sigma$ & Stefan-Boltzmann constant \\ + \hline + \end{tabular} + \caption{Symbols used in above representations of Stefan-Boltzmann law} +\end{table} + +The following plots show the variation of E vs T for a given body with e = 1 in Graph 1 and variation of E vs T for various values of e in graph 2. + +\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/EvsT.eps} +\includegraphics[scale=0.6]{jan-may-2022-latex/AE21B107/variable_e.eps} diff --git a/jan-may-2022-latex/AE21B107/EvsT.eps b/jan-may-2022-latex/AE21B107/EvsT.eps new file mode 100644 index 0000000..814f39a --- /dev/null +++ b/jan-may-2022-latex/AE21B107/EvsT.eps @@ -0,0 +1,2458 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Title: EvsT.eps +%%Creator: Matplotlib v3.5.1, https://matplotlib.org/ +%%CreationDate: Thu Jun 23 01:32:05 2022 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